I just found out that a readymade image of ARM64 Ubuntu Server 18.04 is available for the Raspberry Pi 3! It is available at http://cdimage.ubuntu.com/releases/18.04/beta/. This image also works out of the box with the Pi 3B+. Simply download the image and write it to an SD card just like you would for a Raspbian image.

I installed Ubuntu Server 18.04 ARM64 on my Raspberry Pi 3B using the prebuilt beta image. I installed the Xubuntu desktop, switched to using the Pi's built-in bootloader instead of u-boot, and enabled the VC4 graphics acceleration driver. glxgears gave me around 60fps, and I was able to play Neverball although I had to turn off all the effects like shadows for a smooth experience.

However, Chromium was laggy even when viewing only a couple of webpages. I'd suggest using uBlock Orgin for a smoother experience.

I like this image. It's great for a 64-bit Raspberry Pi server, and can also be used as a desktop setup. This image will work on the Pi 3B+ out of the box so if you're looking to run Ubuntu on your 3B+, then this image is a great way to start.